In mathematics, a pointed set is a set with a distinguished element, which is called the basepoint. Maps of pointed sets (based maps) are those functions that map one basepoint to another, i.e. a map such that . This is usually denoted
- .
Pointed sets may be regarded as a rather simple algebraic structure. In the sense of universal algebra, they are structures with a single nullary operation which picks out the basepoint.
The class of all pointed sets together with the class of all based maps form a category.
A pointed set may be seen as a pointed space under the discrete topology or as a vector space over the field with one element.
Famous quotes containing the words pointed and/or set:
“Punctually at Christmas the soft plush
Of sentiment snows down, embosoms all
The sharp and pointed shapes of venom,”
—William Robert Rodgers (1909–1969)
“All I’m telling you is that that little creature in there has as much right to live as you do. Don’t forget, you invaded his world. You sank a pipe six miles into the ground and when he climbed up you set dogs on him, shot him.”
—Richard Fielding, and Lee Sholem. Superman (George Reeves)